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Use of directions of negative curvature in a modified Newton method

Author
More, J. J.
Published
United States : [publisher not identified], 1977.
[Oak Ridge, Tennessee] : [U.S. Atomic Energy Commission], 1977.
Physical Description
microfiche : negative ; 11 x 15 cm
Additional Creators
Sorensen, D. C.

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Summary
A modified Newton method for the unconstrained minimization problem is presented. The modification occurs in nonconvex regions, where the information contained in the negative eigenvalues of the Hessian is taken into account by performing a line search along a path which is initially tangent to a direction of negative curvature. Termination criteria for the line search are given, and it is proved that the resulting iterates are guaranteed to converge, under reasonable conditions, to a critical point at which the Hessian is positive semidefinite. It is also shown how the Bunch and Parlett decomposition of a symmetric indefinite matrix can be used to give entirely adequate directions of negative curvature.
Report Numbers
ANL-AMD-TM-319
Other Subject(s)
Collection
U.S. Atomic Energy Commission depository collection.
Note
DOE contract number: W-31-109-ENG-38
OSTI Identifier 5331130
Research organization: Argonne National Lab., Ill. (USA).
View MARC record | catkey: 38378943